what is the value of $leftleft(\frac{2}{3}\right)^{0}\right^{-3}$?

Explanation:

Step1: Evaluate inner - exponent

Any non - zero number to the power of 0 is 1. So, $(\frac{2}{3})^0 = 1$.

Step2: Evaluate outer - exponent

We now have $1^{-3}$. According to the negative - exponent rule $a^{-n}=\frac{1}{a^{n}}$, when $a = 1$ and $n = 3$, $1^{-3}=\frac{1}{1^{3}}$. Since $1^{3}=1$, then $\frac{1}{1^{3}} = 1$.

Answer:

1